PhD Chapter 1

Campaign 2014 - Analyses and regressions

This series of files compile analyses done for the specific analysis of Chapter 1, for the local campaign of 2014.

All analyses have been done with PRIMER-e 6 and R 4.1.2.

Click on the table of contents in the left margin to assess a specific analysis.
Click on a figure to zoom it

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We used data from subtidal ecosystems (see metadata files for more information). Only stations that have been sampled both for abiotic parameters and benthic species were included.

Selected variables for the analyses:

Abundances of Bipalponephtys neotena (Bneo) and Spisula solidissima (Ssol) were also considered (see IndVal and SIMPER results).

1. Permutational Analyses of Variance

Results of univariate PermANOVAs on parameters and multivariate PermANOVA on the whole benthic community are presented in the table below. Variables have been standardized by mean and standard-deviation, and taxon densities were (log+1) transformed.

Variable Condition Site(Co) Significative groups of similar sites (p > 0.05)
om S S {HI1 HI2 HI3}, {HI4 R2}, {R1 R2 R3}
gravel S {HI1 HI2 HI3 HI4 R3 R4}, {R1 R2}
sand S All sites in the same group
silt S {HI1 HI2 HI3 HI4 R2 R3}, {R1 R2}, {R1 R4}, {R2 R3 R4}
clay S {HI1 HI2 HI3 HI4}, {HI4 R1 R2 R3 R4}, {R1 R2 R3}, {R3 R4}
arsenic S {HI1 HI2}, {HI3 HI4 R2}, {HI3 HI4 R1 R3 R4}
cadmium S All except {HI1 R2}, {HI1 R3}, {HI2 R2}, {HI2 R3}, {HI3 R2}, {HI3 R3}
chromium S {HI1 HI2 HI3 R1 R4}, {HI4 R2 R3 R4}
copper S S {HI1 HI2 HI3}, {HI1 HI3 HI4}, {HI4 R1 R2}, {R1 R2 R3}, {R2 R3 R4}
iron All except {HI1 R3}, {HI2 R3}, {R1 R3}
manganese S {HI1 HI2}, {HI3 HI4 R1 R4}, {R2 R3}
mercury {HI1 HI2 HI3}, {HI2 HI4 R1 R2 R3 R4}
lead S {HI1 HI2}, {HI1 HI3}, {HI4 R1 R2 R3 R4}
zinc S {HI1 HI2 HI3 HI4}, {HI4 R1 R2 R4}, {HI4 R2 R3 R4}
S (500 µm) S {HI1 HI2 HI3}, {HI4 R1 R3 R4}, {HI4 R2 R3 R4}
N (500 µm) S {HI1 HI2 HI3}, {HI4 R2 R3 R4}, {R1 R4}
H (500 µm) All except {HI2 HI3}, {HI3 HI4}
J (500 µm) S All except {HI1 HI4}, {HI1 R1}, {HI2 HI3}, {HI2 HI4}, {HI2 R1}, {HI2 R2}
ALL SPECIES (500 µm) S S {HI1 HI2}, {R1 R4}, {R2 R3}

2. Similarity and characteristic species

Let’s have a look at the \(\beta\) diversity within our conditions and sites.

Results of the PERMDISP routine are shown below (mean and SE of the deviation from centroid for each group, i.e. multivariate dispersion), along with the mean Bray-Curtis dissimilarity for each group. Taxon densities were (log+1) transformed and PRIMER was used to do the PERMDISP.

Mean within-group Bray-Curtis dissimilarity for each condition or site
  Mean deviation SE of deviation Mean BC dissimilarity
HI 37.2 3.79 0.544
R 49.7 1.81 0.72
P1 22.6 2.47 0.359
P2 21.7 0.28 0.343
P3 18.9 2.73 0.302
P4 48.3 3.39 0.764
R1 44.9 3.85 0.711
R2 40 2.2 0.631
R3 41.2 6.52 0.657
R4 42.5 4.21 0.671

Significative differences in dispersion have been detected between HI and R (p = 0.017), and between {HI1 HI2 HI3} and {HI4 R1 R2 R3 R4} by the PERMDISP and the pairwise tests.

The following analyses allowed to detect species as characteristic of each condition. We used results from PRIMER to justify further their choice.

##                          cluster indicator_value probability
## bipalponephtys_neotena         1          0.9035       0.001
## prionospio_steenstrupi         1          0.8660       0.001
## nephtys_sp                     1          0.8260       0.001
## phoronida                      1          0.7816       0.001
## phyllodoce_groenlandica        1          0.7764       0.001
## capitella_sp                   1          0.7592       0.001
## cirratulidae_spp               1          0.7368       0.001
## limecola_balthica              1          0.7354       0.001
## sarsicytheridea_sp             1          0.6868       0.001
## polychaeta                     1          0.6750       0.001
## scoloplos_armiger              1          0.6743       0.002
## eteone_sp                      1          0.6242       0.001
## hediste_diversicolor           1          0.5500       0.001
## euchone_analis                 1          0.4500       0.001
## pholoe_longa                   1          0.3611       0.041
## pontoporeia_femorata           1          0.3500       0.006
## pholoe_sp                      1          0.3474       0.034
## podocopida                     1          0.3346       0.011
## diastylis_sculpta              1          0.3316       0.010
## glycera_dibranchiata           1          0.3275       0.014
## axinopsida_orbiculata          1          0.3000       0.021
## praxillella_praetermissa       1          0.3000       0.019
## sabellidae_spp                 1          0.3000       0.015
## tharyx_sp                      1          0.3000       0.019
## maldanidae_spp                 1          0.2500       0.047
## spisula_solidissima            2          0.7181       0.001
## echinarachnius_parma           2          0.7000       0.001
## polygordius_sp                 2          0.6005       0.003
## annelida                       2          0.4992       0.001
## cancer_irroratus               2          0.2725       0.040
## 
## Sum of probabilities                 =  98.353 
## 
## Sum of Indicator Values              =  27.96 
## 
## Sum of Significant Indicator Values  =  16.34 
## 
## Number of Significant Indicators     =  30 
## 
## Significant Indicator Distribution
## 
##  1  2 
## 25  5
SIMPER results (mean between-group Bray-Curtis dissimilarity: 0.858)
  average sd ratio ava avb cumsum
bipalponephtys_neotena 0.0603 0.0234 2.58 5.11 0.263 0.0703
nephtys_sp 0.0562 0.0274 2.05 4.77 0.139 0.136
prionospio_steenstrupi 0.0441 0.0179 2.46 3.53 0.139 0.187
phoronida 0.0346 0.0203 1.7 2.94 0.0693 0.227
scoloplos_armiger 0.0341 0.0201 1.7 3.02 0.562 0.267
phyllodoce_groenlandica 0.0311 0.0147 2.12 2.68 0.254 0.303
capitella_sp 0.0298 0.0169 1.76 2.58 0.139 0.338
spisula_solidissima 0.0294 0.0257 1.14 0.235 2.06 0.372
phoxocephalus_holbolli 0.0229 0.0228 1 1.08 1.61 0.399
cirratulidae_spp 0.0228 0.0152 1.5 1.94 0.0347 0.426
limecola_balthica 0.0226 0.0159 1.42 1.75 0.0347 0.452
harpacticoida 0.0219 0.0189 1.16 1.94 1.31 0.477
sarsicytheridea_sp 0.0207 0.0156 1.33 1.81 0.0347 0.502
echinarachnius_parma 0.0201 0.0203 0.995 0 1.4 0.525
eteone_sp 0.0161 0.0131 1.23 1.33 0.0549 0.544
pholoe_minuta_tecta 0.0137 0.0176 0.781 0.883 0.302 0.56
polygordius_sp 0.0137 0.0175 0.78 0.245 0.985 0.576
hediste_diversicolor 0.0135 0.0224 0.602 0.861 0 0.592
euchone_analis 0.0126 0.016 0.79 1.14 0 0.606
pholoe_longa 0.0123 0.0134 0.916 0.972 0.239 0.621
pholoe_sp 0.012 0.0138 0.866 0.954 0.145 0.635
oligochaeta 0.0101 0.0258 0.389 0.278 0.343 0.646
mytilus_sp 0.00938 0.0178 0.528 0.135 0.605 0.657
annelida 0.00902 0.0123 0.736 0.0693 0.681 0.668
podocopida 0.00875 0.0137 0.637 0.755 0.0347 0.678
glycera_sp 0.00863 0.0199 0.435 0.352 0 0.688
pseudoleptocuma_minus 0.00852 0.0124 0.686 0.205 0.42 0.698
sabellidae_spp 0.00822 0.0137 0.598 0.727 0 0.707
pontoporeia_femorata 0.00794 0.0119 0.667 0.643 0 0.717
microphthalmus_sczelkowii 0.00775 0.013 0.596 0.609 0.0896 0.726
diastylis_sculpta 0.00738 0.0111 0.668 0.626 0.0347 0.734
spio_filicornis 0.00706 0.0111 0.637 0.355 0.139 0.743
aricidea_sp 0.00699 0.0117 0.6 0.554 0.0896 0.751
tharyx_sp 0.00686 0.0113 0.609 0.534 0 0.759
polychaeta 0.00675 0.00638 1.06 0.624 0.208 0.767
nephtys_caeca 0.00653 0.00968 0.674 0.199 0.283 0.774
glycera_dibranchiata 0.00636 0.00864 0.737 0.504 0.0347 0.782
solenoidea 0.00627 0.00958 0.655 0.425 0.139 0.789
praxillella_praetermissa 0.00618 0.00979 0.631 0.545 0 0.796
axinopsida_orbiculata 0.00615 0.0102 0.6 0.542 0 0.803
bivalvia 0.00597 0.0093 0.642 0.351 0.167 0.81
hemicythere_villosa 0.00579 0.0106 0.547 0.339 0.199 0.817
spiophanes_bombyx 0.00564 0.0122 0.461 0.104 0.219 0.824
halacaridae_spp 0.00549 0.012 0.458 0 0.414 0.83
phyllodoce_sp 0.00509 0.0117 0.435 0.145 0.194 0.836
cancer_irroratus 0.00482 0.00769 0.626 0.0805 0.283 0.841
eucratea_loricata 0.00478 0.00676 0.707 0.243 0.173 0.847
sertulariidae_spp 0.00474 0.00678 0.7 0.555 0.451 0.853
microphthalmus_sp 0.0047 0.00968 0.486 0.42 0 0.858
caprella_septentrionalis 0.00439 0.0148 0.296 0 0.314 0.863
edotia_triloba 0.00423 0.00765 0.553 0.115 0.214 0.868
psammonyx_nobilis 0.00408 0.00939 0.434 0.0693 0.159 0.873
maldanidae_spp 0.00376 0.00688 0.546 0.305 0 0.877
aricidea_acmira_catherinae 0.00337 0.00911 0.37 0.0973 0.145 0.881
cylichna_alba 0.00297 0.00717 0.415 0.271 0 0.885
capitellidae_spp 0.00288 0.00778 0.37 0.19 0.0347 0.888
brachyura 0.00257 0.00623 0.413 0.196 0 0.891
obelia_sp 0.00256 0.00542 0.473 0.0347 0.139 0.894
spionidae_spp 0.00256 0.00506 0.506 0.0549 0.159 0.897
campanulariidae_spp 0.0025 0.0053 0.472 0.658 0.555 0.9

3. Regressions

3.1. Data manipulation

For the following analyses, independant variables are habitat parameters and heavy metal concentrations, dependant variables are diversity indices. Variables have been standardized by mean and standard-deviation.

3.1.1. Identification of outliers

To identify stations that are not consistent with the others, we used the multivariate Cook’s Distance (CD) on the uncorrelated variables. A significative threshold of 4 times the mean of CD has been established.

We identified stations 1 and 29 as general outliers. They have been deleted for the following analyses.

3.1.2. Correlations between predictors

Correlations have been calculated with Spearman’s rank coefficient.

According to these results, the following variables are highly correlated (\(|\rho|\) > 0.80) so they have been considered together in the regressions:

  • cadmium, chromium and manganese concentrations (cadmium and manganese deleted)
  • lead and zinc concentrations (zinc deleted)

We also decided to exclude clay content in the regressions, as it tends to increase drasticaly VIFs due to a marginal negative correlation with sand (very high \(R^{2}\)).

Correlation coefficients between habitat parameters and metals concentrations
  om gravel sand silt clay arsenic cadmium chromium copper iron manganese mercury lead zinc
om 1 -0.562 -0.118 -0.361 0.545 0.565 0.324 0.206 0.786 -0.123 0.363 0.701 0.656 0.676
gravel -0.562 1 0.243 0.344 -0.752 -0.417 -0.211 -0.134 -0.498 -0.046 -0.379 -0.516 -0.506 -0.544
sand -0.118 0.243 1 -0.616 -0.66 -0.327 -0.478 -0.554 -0.405 -0.543 -0.506 -0.287 -0.418 -0.464
silt -0.361 0.344 -0.616 1 -0.138 -0.13 0.284 0.394 -0.111 0.328 0.077 -0.19 -0.045 -0.018
clay 0.545 -0.752 -0.66 -0.138 1 0.577 0.406 0.381 0.629 0.368 0.598 0.606 0.638 0.663
arsenic 0.565 -0.417 -0.327 -0.13 0.577 1 0.466 0.403 0.672 0.279 0.571 0.581 0.654 0.589
cadmium 0.324 -0.211 -0.478 0.284 0.406 0.466 1 0.865 0.528 0.6 0.796 0.462 0.808 0.792
chromium 0.206 -0.134 -0.554 0.394 0.381 0.403 0.865 1 0.463 0.766 0.798 0.456 0.761 0.739
copper 0.786 -0.498 -0.405 -0.111 0.629 0.672 0.528 0.463 1 0.234 0.577 0.648 0.725 0.832
iron -0.123 -0.046 -0.543 0.328 0.368 0.279 0.6 0.766 0.234 1 0.68 0.136 0.459 0.446
manganese 0.363 -0.379 -0.506 0.077 0.598 0.571 0.796 0.798 0.577 0.68 1 0.591 0.798 0.757
mercury 0.701 -0.516 -0.287 -0.19 0.606 0.581 0.462 0.456 0.648 0.136 0.591 1 0.726 0.661
lead 0.656 -0.506 -0.418 -0.045 0.638 0.654 0.808 0.761 0.725 0.459 0.798 0.726 1 0.921
zinc 0.676 -0.544 -0.464 -0.018 0.663 0.589 0.792 0.739 0.832 0.446 0.757 0.661 0.921 1

3.2. Univariate regressions

We used linear models for the regressions on diversity indices. Outliers and correlated variables were removed from these analyses. Variables have been standardized by mean and standard-deviation (coefficients need to be back-transformed to be used in predictive models).

3.2.1. Simple regressions

These analyses have been done to explore the relationships between variables. As it is a huge number of results to interpret, only multiple regressions will be included in the article.

Adjusted R-squared of simple regressions with all variables
  om gravel sand silt arsenic chromium copper iron mercury lead
S 0.2614 0.07195 -0.02463 0.2452 0.2742 -0.02566 0.3224 -0.009631 0.2168 0.3111
N 0.4527 0.1632 0.03359 0.2031 0.5568 0.1578 0.6478 -0.02778 0.2666 0.7254
H -0.02759 -0.02024 -0.02717 -0.02656 0.01357 0.09775 -0.02313 -0.02743 -0.02778 0.02136
J 0.07927 0.04049 -0.02664 0.05976 0.2216 0.06225 0.1316 -0.01732 0.04197 0.2407
p-values of simple regressions with all variables
  om gravel sand silt arsenic chromium copper iron mercury lead
S 0.0006134 0.05695 0.7414 0.00093 0.0004393 0.7865 0.0001196 0.4264 0.001894 0.0001634
N 2.223e-06 0.006893 0.1393 0.002651 4.565e-08 0.007834 6.818e-10 0.993 0.0005358 7.372e-12
H 0.935 0.6092 0.8847 0.8374 0.2273 0.0315 0.6884 0.9123 0.9951 0.1872
J 0.04813 0.1182 0.843 0.07542 0.00168 0.0712 0.01443 0.5469 0.1142 0.001041

3.2.2. Multiple regressions: best model selection

This section presents analyses done to determine (i) which model (metals, parameters or all) decribes the best the parameters and (ii) which variables are the most important to explain the parameters.

The aim here is to know which model is the best to explain our data.

Richness
  n df AIC ∆AIC R2adj
Full model 38 12 97.27 6.963 0.44
Parameters 38 6 99.41 9.101 0.34
Metals 38 8 90.3 0 0.5
Density
  n df AIC ∆AIC R2adj
Full model 38 12 60.4 0 0.78
Parameters 38 6 84.97 24.57 0.54
Metals 38 8 60.82 0.4177 0.77
Diversity
  n df AIC ∆AIC R2adj
Full model 38 12 118.5 5.511 0.05
Parameters 38 6 119.5 6.562 -0.09
Metals 38 8 113 0 0.12
Evenness
  n df AIC ∆AIC R2adj
Full model 38 12 112.2 5.187 0.18
Parameters 38 6 113.4 6.413 0.05
Metals 38 8 107 0 0.23

3.2.3. Multiple regressions: significant variables selection

We identified which variables were selected after an AIC procedure to predict the best the parameters. Results of the variable selection, according to AIC, and details of the regressions, with diagnostics and cross-validation, are summarized below.

All variables
Variable (or combination) S N H J
om +
gravel +
sand/clay - -
silt -
arsenic + - -
chromium/cadmium/manganese - + - -
copper +
iron - + +
mercury +
lead/zinc + +
Adjusted \(R^{2}\) 0.55 0.79 0.17 0.28
Richness
## FULL MODEL
## Adjusted R2 is: 0.44
Fitting linear model: S ~ om + gravel + sand + silt + arsenic + chromium + copper + iron + mercury + lead
  Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.2146 0.2632 0.815 0.4222
om -0.1245 0.2954 -0.4215 0.6767
gravel 0.7738 1.399 0.5529 0.5849
sand -0.1234 0.2005 -0.6158 0.5432
silt -0.1265 0.2078 -0.6086 0.5479
arsenic -0.06305 0.3048 -0.2068 0.8377
chromium -0.6247 0.3274 -1.908 0.06702
copper -0.0802 0.3662 -0.219 0.8283
iron -0.02247 0.1681 -0.1337 0.8946
mercury 0.6446 0.5486 1.175 0.2502
lead 1.026 0.6953 1.475 0.1517 
## RMSE from cross-validation: 1.196093
Variance Inflation Factors
  om gravel sand silt arsenic chromium copper iron mercury lead
VIF 2.43 1.47 1.66 1.7 2.47 2.69 2.97 1.39 2.05 5.61 

## REDUCED MODEL
## Adjusted R2 is: 0.55
Fitting linear model: S ~ chromium + mercury + lead
  Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.06598 0.116 0.569 0.5731
chromium -0.5891 0.1501 -3.926 0.0004006 * * *
mercury 0.4833 0.2745 1.761 0.08726
lead 0.8854 0.1679 5.274 7.578e-06 * * * 
## RMSE from cross-validation: 1.056735
Variance Inflation Factors
  chromium mercury lead
VIF 1.37 1.13 1.5

Density
## FULL MODEL
## Adjusted R2 is: 0.78
Fitting linear model: N ~ om + gravel + sand + silt + arsenic + chromium + copper + iron + mercury + lead
  Estimate Std. Error t value Pr(>|t|)
(Intercept) -0.1107 0.1621 -0.6829 0.5005
om 0.3911 0.1818 2.151 0.04061 *
gravel -0.5637 0.8615 -0.6543 0.5185
sand -0.01695 0.1234 -0.1374 0.8918
silt -0.1169 0.1279 -0.9143 0.3687
arsenic 0.2955 0.1877 1.575 0.127
chromium 0.1019 0.2015 0.5057 0.6172
copper 0.1279 0.2254 0.5676 0.575
iron -0.1257 0.1035 -1.214 0.2352
mercury -0.2897 0.3377 -0.8577 0.3986
lead 0.2056 0.4281 0.4804 0.6348 
## RMSE from cross-validation: 0.750523
Variance Inflation Factors
  om gravel sand silt arsenic chromium copper iron mercury lead
VIF 2.43 1.47 1.66 1.7 2.47 2.69 2.97 1.39 2.05 5.61 

## REDUCED MODEL
## Adjusted R2 is: 0.79
Fitting linear model: N ~ om + silt + arsenic + chromium + copper + iron
  Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.01572 0.07352 0.2139 0.832
om 0.3026 0.09456 3.2 0.003167 * *
silt -0.1786 0.08945 -1.997 0.05468
arsenic 0.3646 0.1159 3.145 0.00365 * *
chromium 0.1814 0.1123 1.614 0.1166
copper 0.2154 0.1369 1.574 0.1257
iron -0.1261 0.09095 -1.386 0.1755 
## RMSE from cross-validation: 0.690898
Variance Inflation Factors
  om silt arsenic chromium copper iron
VIF 1.3 1.22 1.56 1.54 1.85 1.25

Diversity
## FULL MODEL
## Adjusted R2 is: 0.05
Fitting linear model: H ~ om + gravel + sand + silt + arsenic + chromium + copper + iron + mercury + lead
  Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.3214 0.348 0.9237 0.3638
om -0.1565 0.3904 -0.4009 0.6916
gravel 1.722 1.85 0.9311 0.36
sand -0.2678 0.265 -1.011 0.3212
silt 0.02221 0.2747 0.08088 0.9361
arsenic -0.5028 0.4029 -1.248 0.2228
chromium -0.9681 0.4327 -2.237 0.03371 *
copper 0.1013 0.484 0.2092 0.8359
iron 0.3639 0.2222 1.638 0.1131
mercury 0.3504 0.7251 0.4832 0.6329
lead 0.7228 0.9191 0.7864 0.4385 
## RMSE from cross-validation: 1.326798
Variance Inflation Factors
  om gravel sand silt arsenic chromium copper iron mercury lead
VIF 2.43 1.47 1.66 1.7 2.47 2.69 2.97 1.39 2.05 5.61 

## REDUCED MODEL
## Adjusted R2 is: 0.17
Fitting linear model: H ~ gravel + sand + arsenic + chromium + iron + lead
  Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.3127 0.2695 1.16 0.2548
gravel 1.941 1.427 1.36 0.1835
sand -0.2974 0.1863 -1.596 0.1206
arsenic -0.4728 0.3203 -1.476 0.15
chromium -0.9665 0.2956 -3.27 0.002635 * *
iron 0.3668 0.1979 1.854 0.07331
lead 0.7646 0.4328 1.767 0.08711 
## RMSE from cross-validation: 1.066136
Variance Inflation Factors
  gravel sand arsenic chromium iron lead
VIF 1.21 1.24 2.09 1.96 1.32 2.81

Evenness
## FULL MODEL
## Adjusted R2 is: 0.18
Fitting linear model: J ~ om + gravel + sand + silt + arsenic + chromium + copper + iron + mercury + lead
  Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.2272 0.3204 0.709 0.4844
om -0.1924 0.3595 -0.5352 0.5969
gravel 1.286 1.703 0.755 0.4568
sand -0.2388 0.244 -0.9784 0.3366
silt 0.08012 0.2529 0.3168 0.7538
arsenic -0.4975 0.3711 -1.341 0.1912
chromium -0.4977 0.3985 -1.249 0.2223
copper 0.05134 0.4457 0.1152 0.9092
iron 0.2896 0.2046 1.415 0.1684
mercury 0.1629 0.6678 0.2439 0.8092
lead 0.2292 0.8464 0.2708 0.7886 
## RMSE from cross-validation: 1.002764
Variance Inflation Factors
  om gravel sand silt arsenic chromium copper iron mercury lead
VIF 2.43 1.47 1.66 1.7 2.47 2.69 2.97 1.39 2.05 5.61 

## REDUCED MODEL
## Adjusted R2 is: 0.28
Fitting linear model: J ~ sand + arsenic + chromium + iron
  Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.00684 0.1395 0.04904 0.9612
sand -0.224 0.1677 -1.336 0.1907
arsenic -0.4449 0.1602 -2.778 0.008952 * *
chromium -0.358 0.1934 -1.851 0.0732
iron 0.2699 0.1701 1.587 0.1221 
## RMSE from cross-validation: 0.9386957
Variance Inflation Factors
  sand arsenic chromium iron
VIF 1.21 1.14 1.4 1.23

Parameters
Variable (or combination) S N H J
om + + -
gravel
sand/clay -
silt - -
Adjusted \(R^{2}\) 0.36 0.55 0 0.08
Richness
## FULL MODEL
## Adjusted R2 is: 0.34
Fitting linear model: S ~ om + gravel + sand + silt
  Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.02794 0.2434 0.1148 0.9093
om 0.3383 0.1531 2.209 0.03421 *
gravel 0.175 1.284 0.1363 0.8924
sand -0.1469 0.1649 -0.8906 0.3796
silt -0.4431 0.185 -2.395 0.02246 * 
## RMSE from cross-validation: 0.9300972
Variance Inflation Factors
  om gravel sand silt
VIF 1.16 1.24 1.25 1.39 

## REDUCED MODEL
## Adjusted R2 is: 0.36
Fitting linear model: S ~ om + silt
  Estimate Std. Error t value Pr(>|t|)
(Intercept) -0.004759 0.1309 -0.03635 0.9712
om 0.3875 0.1407 2.753 0.009287 * *
silt -0.3649 0.1414 -2.582 0.01418 * 
## RMSE from cross-validation: 0.8989986
Variance Inflation Factors
  om silt
VIF 1.08 1.08

Density
## FULL MODEL
## Adjusted R2 is: 0.54
Fitting linear model: N ~ om + gravel + sand + silt
  Estimate Std. Error t value Pr(>|t|)
(Intercept) -0.0727 0.2013 -0.3611 0.7203
om 0.4731 0.1266 3.736 0.0007077 * * *
gravel -0.5186 1.062 -0.4885 0.6285
sand -0.2515 0.1364 -1.844 0.07419
silt -0.342 0.153 -2.235 0.03231 * 
## RMSE from cross-validation: 0.91835
Variance Inflation Factors
  om gravel sand silt
VIF 1.16 1.24 1.25 1.39 

## REDUCED MODEL
## Adjusted R2 is: 0.55
Fitting linear model: N ~ om + sand + silt
  Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.009598 0.1089 0.08811 0.9303
om 0.475 0.1252 3.795 0.0005805 * * *
sand -0.2793 0.1225 -2.279 0.02906 *
silt -0.3791 0.1313 -2.888 0.006695 * * 
## RMSE from cross-validation: 0.9212626
Variance Inflation Factors
  om sand silt
VIF 1.16 1.14 1.21

Diversity
## FULL MODEL
## Adjusted R2 is: -0.09
Fitting linear model: H ~ om + gravel + sand + silt
  Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.2396 0.3172 0.7553 0.4554
om -0.04775 0.1995 -0.2393 0.8123
gravel 1.383 1.673 0.8268 0.4143
sand -0.133 0.2149 -0.6188 0.5403
silt -0.1739 0.2411 -0.7212 0.4759 
## RMSE from cross-validation: 1.237837
Variance Inflation Factors
  om gravel sand silt
VIF 1.16 1.24 1.25 1.39 

## REDUCED MODEL
## Adjusted R2 is: 0
Fitting linear model: H ~ 1
  Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.01659 0.1658 0.1001 0.9208 
## RMSE from cross-validation: 1.027593

Quitting from lines 404-406 (C1_analyses_14B.Rmd) Erreur dans h(simpleError(msg, call)) : erreur d’�valuation de l’argument ‘x’ lors de la s�lection d’une m�thode pour la fonction ‘t’ : erreur d’�valuation de l’argument ‘x’ lors de la s�lection d’une m�thode pour la fonction ‘as.data.frame’ : indice hors limites De plus : Il y a eu 22 avis (utilisez warnings() pour les visionner)

Evenness
## FULL MODEL
## Adjusted R2 is: 0.05
Fitting linear model: J ~ om + gravel + sand + silt
  Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.2087 0.2928 0.713 0.4809
om -0.247 0.1842 -1.341 0.189
gravel 1.189 1.544 0.7698 0.4469
sand -0.07851 0.1983 -0.3958 0.6948
silt 0.105 0.2225 0.472 0.64 
## RMSE from cross-validation: 1.056183
Variance Inflation Factors
  om gravel sand silt
VIF 1.16 1.24 1.25 1.39 

## REDUCED MODEL
## Adjusted R2 is: 0.08
Fitting linear model: J ~ om
  Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.0259 0.1575 0.1644 0.8703
om -0.3206 0.1567 -2.046 0.04813 * 
## RMSE from cross-validation: 0.986031
Variance Inflation Factors
  om
VIF 1

Metals
Variable (or combination) S N H J
arsenic -
chromium/cadmium/manganese - - -
copper +
iron + + +
mercury + +
lead/zinc + + -
Adjusted \(R^{2}\) 0.55 0.78 0.14 0.27
Richness
## FULL MODEL
## Adjusted R2 is: 0.5
Fitting linear model: S ~ arsenic + chromium + copper + iron + mercury + lead
  Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.0652 0.1222 0.5334 0.5975
arsenic -0.008109 0.2435 -0.03331 0.9736
chromium -0.5947 0.2082 -2.857 0.007575 * *
copper 0.01552 0.271 0.05725 0.9547
iron 0.009241 0.1434 0.06443 0.949
mercury 0.4821 0.2922 1.65 0.109
lead 0.8805 0.4411 1.996 0.05477 
## RMSE from cross-validation: 1.152864
Variance Inflation Factors
  arsenic chromium copper iron mercury lead
VIF 2.08 1.81 2.32 1.25 1.15 3.76 

## REDUCED MODEL
## Adjusted R2 is: 0.55
Fitting linear model: S ~ chromium + mercury + lead
  Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.06598 0.116 0.569 0.5731
chromium -0.5891 0.1501 -3.926 0.0004006 * * *
mercury 0.4833 0.2745 1.761 0.08726
lead 0.8854 0.1679 5.274 7.578e-06 * * * 
## RMSE from cross-validation: 1.056735
Variance Inflation Factors
  chromium mercury lead
VIF 1.37 1.13 1.5

Density
## FULL MODEL
## Adjusted R2 is: 0.77
Fitting linear model: N ~ arsenic + chromium + copper + iron + mercury + lead
  Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.05559 0.08292 0.6704 0.5076
arsenic 0.06272 0.1652 0.3797 0.7067
chromium -0.1472 0.1412 -1.042 0.3053
copper 0.091 0.1839 0.4949 0.6242
iron -0.1017 0.0973 -1.045 0.3042
mercury 0.3282 0.1982 1.656 0.1078
lead 0.7754 0.2993 2.591 0.01446 * 
## RMSE from cross-validation: 0.7234506
Variance Inflation Factors
  arsenic chromium copper iron mercury lead
VIF 2.08 1.81 2.32 1.25 1.15 3.76 

## REDUCED MODEL
## Adjusted R2 is: 0.78
Fitting linear model: N ~ chromium + mercury + lead
  Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.05669 0.08039 0.7052 0.4855
chromium -0.2516 0.104 -2.418 0.02111 *
mercury 0.3349 0.1903 1.76 0.08738
lead 0.9585 0.1164 8.235 1.312e-09 * * * 
## RMSE from cross-validation: 0.4905408
Variance Inflation Factors
  chromium mercury lead
VIF 1.37 1.13 1.5

Diversity
## FULL MODEL
## Adjusted R2 is: 0.12
Fitting linear model: H ~ arsenic + chromium + copper + iron + mercury + lead
  Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.01703 0.1647 0.1034 0.9183
arsenic -0.2658 0.328 -0.8102 0.424
chromium -0.601 0.2805 -2.143 0.0401 *
copper 0.4598 0.3652 1.259 0.2174
iron 0.3718 0.1932 1.924 0.0636
mercury 0.1633 0.3936 0.4149 0.681
lead -0.11 0.5943 -0.1851 0.8544 
## RMSE from cross-validation: 1.172167
Variance Inflation Factors
  arsenic chromium copper iron mercury lead
VIF 2.08 1.81 2.32 1.25 1.15 3.76 

## REDUCED MODEL
## Adjusted R2 is: 0.14
Fitting linear model: H ~ chromium + iron
  Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.01129 0.154 0.07331 0.942
chromium -0.5118 0.1825 -2.804 0.008169 * *
iron 0.2954 0.1817 1.626 0.113 
## RMSE from cross-validation: 0.9944238
Variance Inflation Factors
  chromium iron
VIF 1.19 1.19

Evenness
## FULL MODEL
## Adjusted R2 is: 0.23
Fitting linear model: J ~ arsenic + chromium + copper + iron + mercury + lead
  Estimate Std. Error t value Pr(>|t|)
(Intercept) -0.01419 0.1523 -0.09316 0.9264
arsenic -0.2487 0.3034 -0.8198 0.4186
chromium -0.1171 0.2594 -0.4515 0.6548
copper 0.3649 0.3377 1.081 0.2882
iron 0.298 0.1787 1.668 0.1054
mercury -0.08445 0.364 -0.232 0.8181
lead -0.5994 0.5496 -1.09 0.2839 
## RMSE from cross-validation: 1.018418
Variance Inflation Factors
  arsenic chromium copper iron mercury lead
VIF 2.08 1.81 2.32 1.25 1.15 3.76 

## REDUCED MODEL
## Adjusted R2 is: 0.27
Fitting linear model: J ~ iron + lead
  Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.01118 0.1405 0.07954 0.9371
iron 0.2188 0.1424 1.536 0.1335
lead -0.5669 0.1461 -3.88 0.0004409 * * * 
## RMSE from cross-validation: 0.8952223
Variance Inflation Factors
  iron lead
VIF 1.02 1.02

3.3. Multivariate regression

Independant variables are habitat parameters and heavy metal concentrations, dependant variables are species abundances. Variables have been standardized by mean and standard-deviation, and outliers and correlated variables have been excluded. Taxon densities were (log+1) transformed.

This analysis has been done on PRIMER, with a DistLM to identify the variables that explain the most the community variability and with a dbRDA to plot the results.

Variables selected by the DistLM procedure have a \(R^{2}\) of 0.4.

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